Question

What is a recursive formula for a geometric sequence?

Answer 1

Recursive formula for a geometric sequence is `a_n=a_(n-1)xxr`, where `r` is the common ratio.

Explanation:

A geometric series is of the form

`a,ar,ar^2,ar^3,ar^4,ar^5.........................`

in which first term `a_1=a` and other terms are obtained by multiplying by `r`.

Observe that each term is `r` times the previous term. Hence to get `n^(th)` term we multiply `(n-1)^(th)` term by `r`

i.e. `a_n=a_(n-1)xxr`

This is called recursive formula for geometric sequence.

There is also explicit formula for `n^(th)` term i.e. `a_n=axxr^(n-1)`